"We would be disappointed if we didn't go through to the second round," he said. "We're confident. We played five tough games against top European teams in our preparation and apart from the Greek game we've competed very well in all."
The Tall Blacks shared a two-game series against Serbia to cap their build-up, after narrowly losing to Lithuania and Slovenia. All three opponents will play at the World Cup. Lithuania is viewed as one of the contenders for the title, having won bronze in 2010 and silver at last year's European championships.
To achieve their goal of making the second round, Vucinic's side will need to finish in the top four of Group C, featuring the 2010 finalists, the USA and Turkey, Ukraine, Finland, and the Dominican Republic.
"Obviously the United States is a favourite against anybody, but I feel in all of the other games if we play well we're going to win," Vucinic said. "It's a double-edged sword and it's [up to us] how we perform on the night."
First up for the Tall Blacks is Turkey, who are ranked seventh in the world but failed to get out of their group at the European champs.
With giant New Orleans Pelicans centre Omer Asik patrolling the paint for Turkey, the onus will again fall on New Zealand's guards.
Kirk Penney, the second leading scorer from the 2010 world championships, will carry the scoring burden, with help from the Websters. Teenager Tai Webster has won the starting point guard role from Lindsay Tait, while older brother Corey Webster will be one of the first players off New Zealand's bench.
Corey Webster says it's his job to be a spark when he checks into the game.
"A bit of instant scoring, a little bit of defensive pressure and stuff like that," he said. "I'm always anxious waiting on the bench to get in the game but when my time comes I'm ready."
After missing the 2010 tournament following a positive test for cannabis, Corey Webster rates being selected to the Tall Blacks' Basketball World Cup as the biggest achievement of his career so far.
"Being able to represent your country at a World Cup tournament is everything you dream of really, so I'm just soaking it up."